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**Additional info for Comprehensive Nuclear Materials, Volume 1: Basic Aspects of Radiation Effects in Solids / Basic Aspects of Multi-Scale Modeling**

**Sample text**

We have seen that for fcc crystals there are pairs of opposite jump directions that have identical transformation mn , but they differ only in the signs of the strain values epq jump vector components Xk. Hence, these opposite pairs of jump directions cancel each other’s contribution to the sum in eqn [86]. As a result, there is no correction to the diffusion tensor that is linear in stress gradients. Spatially varying stress field, however, produce a drift force. Inserting eqn [84] into the formula [77] leads to @spq L0 X mn Xi Xk epq Fi ¼ ÀbO @xk 2n R;m;n h i f S ½87 exp ÀbEmn ðrÞ þ bE ðrÞ The factor with the sum has a remarkable resemblance with the expression for the diffusion tensor.

The numerical solutions of US(R þ h0) ¼ 0 and of UV(RÀh0) ¼ 0 gives the results for h0/r0 shown in Figure 17. There is a modest dependence on the radius of curvature of the surface. Approximately, however, the defect strain energy becomes zero about halfway between the top and first subsurface atomic layer, assuming that r0 is equal to the atomic radius. 55 1 10 100 Surface radius/atomic radius 1000 Figure 17 Distance to surface where the defect strain energy disappears. dislocations and interfaces in the material is the most essential process that restores the material to its almost normal state.

III/25. W % Àui0 ðrd Þ The first term vanishes because the sum of Kanzaki forces is zero, as pointed out in eqn [B4], and the second term can be expressed in terms of the dipole tensor defined in [B6]. 083 17 fi ðÞ ðÞ Rj À Á Á Á ½41 1 ½45 W ¼ À V rel s0kk 3 In this last form, we used the notation for the relaxation volume for the misfit or transformation volume, that is, DV ¼ V rel, to emphasize the fact that the interaction energy of vacancies and self-interstitials does not depend on their formation volumes, but on their relaxation volumes.